Finite Group DatabasebetaFinite Group Databasebeta| order | 18752 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #97×C293 ⋊ C2 |
| Sylow | C293 ⋊ C4×M16 |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9376 |
Polycyclic presentation:
2^6,293|a^2=d,b^2=e,d^2=f,c^a=cf,g^b=g^292,g^c=g^2922960 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49157370, #49157372, #49157375, … |
| maximal normal subgroup of | #49157370, #49157372, #49157375, … |
| maximal quotient of | #49157064, #49157073, #49157081, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18752, 501);